Can a deep neural network be trained to classify an integer N1 as being divisible by another integer N2?
There is a recent development in research that was looking into effectiveness of neural networks on arithmetic. Interestingly, feed-forward neural networks (MLPs) with various activation functions as well as LSTMs (RNNs which are Turing-complete) are not able to model simple arithmetic operations (e.g. addition/multiplication), they designed a new logic unit which can solve all of the simple arithmetic problems.

See: Neural Arithmetic Logic Units

More recently, DL can solve symbolic maths: Deep Learning for Symbolic Mathematics